FE Environmental Thermodynamics Practice Problems

The current FE Environmental specification assigns 3-5 of the 110 exam questions to Thermodynamics. Form A contains 3 original problems in this area. The sample below is published in full, with the same worked-solution format used throughout the book.

A morning sounding at a proposed incinerator site records air temperatures of $21. 3^{\circ} C$ at 10 m and $19. 0^{\circ} C$ at 160 m above grade. The dry adiabatic lapse rate is $9. 8^{\circ} C$ /km. Which of the following best describes the stability of the layer and the expected stack plume behavior?

(A)Superadiabatic and unstable; looping plume
(B)Neutral; coning plume
(C)Subadiabatic and stable; fanning plume
(D)Temperature inversion; ground-level fumigation

Show worked solution

Answer: (A)

The layer cools at $15. 3^{\circ} C$ /km, much steeper than the dry adiabatic $9. 8^{\circ} C$ /km, so displaced parcels stay buoyant and the plume loops.

Stability is judged by the environmental lapse rate measured across the sounding layer.

Γ = \frac{21.3 - 19.0}{160 - 10} \times 1000 = 15. 3^{\circ} C/km

A parcel cooling at the dry adiabatic rate rises into air that has cooled faster, so it stays warmer and lighter than its surroundings and the strong vertical motion drives the plume into a looping pattern.

Γ = 15.3 > Γ_{d} = 9. 8^{\circ} C/km

FE Reference Handbook — Environmental Engineering: Atmospheric Stability, Dry Adiabatic Lapse Rate

Why the other choices appear

(B)Follows from treating any temperature decrease with height as adiabatic by default, without evaluating 2.3 °C over 0.150 km = 15.3 °C/km against 9.8 °C/km.
(C)Comes from comparing the raw 2.3 °C temperature drop with the 9.8 °C/km rate without converting the 150 m layer thickness to kilometers.
(D)Comes from reversing the two readings so temperature appears to rise with height.